Abstract
We propose a transfer-matrix theory to reveal the hidden structure in the multipartite nonlocality operators in one-dimensional (1D) quantum chains. The theory offers a unified description for the scaling behaviors of multipartite quantum nonlocality in general 1D quantum lattices. Furthermore, in order to figure out the hierarchy of multipartite nonlocality for infinite-size chains, powerful transfer-matrix-based algorithms are proposed. In quantum critical regions, the algorithms converge much faster than the traditional approach.
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